I think your hunch is right, but economists' definitions do tend to be tied to numbers. Pew Research and others -- although I doubt this is a universal definition—usually treat "middle class" as being two-thirds to double the median income in an area. That seems like an unusually high range -- I would have assumed two-thirds to four-thirds would make more sense, but I suspect it's to account for how sharply incomes rise at the high end of the scale (e.g., the median salary in the top quintile compared to that of the middle quintile is many times greater than the median salary in the middle quintile is compared to the lowest).

Even with that there's an awful lot of caveats, though; as folks have noted, regional differences can be huge. The median income in Silicon Valley as of last year is just under $100K (despite the picture that Hacker News can sometimes paint!), but in Tampa Bay, Florida, it was just under $60K.